Download pdf - 12.3 Surface Areas of Pyramids and Cones Goals Students ......GH Lesson 12 3_notes.notebook March 29, 2016 12.3 Surface Areas of Pyramids and Cones Goals Students will be able to

GHLesson 123_notes.notebook March 29, 2016

12.3 Surface Areas of Pyramids and Cones

Goals

Students will be able to . . .

• find lateral areas and surface areas of pyramids.

• find lateral areas and surface areas of cones.

Pyramid 3D object in which one face can be any polygon and the other faces are triangles that meet at a common vertex.

Base can be any polygon

Lateral faces faces that are not the base (triangles)

Lateral faces will be isosceles triangles if the base is a regular polygon.


HeightSlantheighth l

Vertex the point where all the lateral faces meet

Height (h) perpendicular distance from the vertex to the base

When the pyramid is a right pyramid the altitude connects the vertex and center of the base.

Slant height (l ) the height of a lateral face (triangle) of the pyramid

Square pyramid

Square Base

Right Triangle May need to use Pythagorean Theorem, Trigonometry or Special Right Triangles to find an unknown dimension.


ss

ss

l

l

ll

Using the net of a pyramid, find the equation for the Lateral Area.

L =

1 2

S = pl + B

Vertex

Altitude

Base edge

Lateral edge

lRegular Hexagonal Pyramid


Cone is a solid with a circular base and a vertex (there are no polygons).

Height (right cone) the perpendicular distance from the vertex to the center of the base.

Slant height the distance from the vertex to any point on the edge of the base.

S = πrl + B


Practice 123

